Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[{x}^{3} + {x}^{2}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
{x}^{3} + {x}^{2}
double code(double x) {
	return ((x * (x * x)) + (x * x));
}
↓
double code(double x) {
	return (pow(x, 3.0) + pow(x, 2.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x \cdot x + x\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot \left(x \cdot x\right) + x \cdot x}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{{x}^{3}} + x \cdot x\]

  6. Simplified0.0

    \[\leadsto {x}^{3} + \color{blue}{{x}^{2}}\]

  7. Final simplification0.0

    \[\leadsto {x}^{3} + {x}^{2}\]

Reproduce

herbie shell --seed 2020091 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

  (+ (* x (* x x)) (* x x)))